As part of the natural evolution and continued optimisation of their designs, current and future magnetic recording heads, used and proposed in technologies such as perpendicular recording, shingled magnetic recording and two-dimensional magnetic recording, often exhibit asymmetry in their structure. They consist of two semi-infinite poles separated by a gap (where the recording field is produced), with an inner gap faces inclined at an angle. Modelling of the fields from asymmetrical structures is complex, and no explicit solutions are currently available (only implicit conformal mapping solutions are available for rational inclination angles). Moreover, there is limited understanding on the correlation between the gap corner angle and the magnitude, distribution and wavelength response of these head structures. This research was therefore set out to investigate approximate analytical and semi-analytical methods for modelling the magnetic potentials and fields of two-dimensional symmetrical and asymmetrical magnetic recording heads, and deliver a quantitative understanding of the behaviour of the potentials and fields as functions of gap corner angles. The accuracy of the derived expressions (written in terms of the normalised root-mean-square deviation) was assessed by comparison to exact available solutions for limited cases, and to finite-element calculations on Comsol Multiphysics. Two analytical methods were derived to approximately model the fields from two-dimensional heads with tilted gap corners in the presence and absence of a soft magnetic underlayer (SUL): in the first method, the potential near a single, two-dimensional corner held at a constant potential is derived exactly through solution of Laplace's equation for the scalar potential in polar coordinates. Then through appropriate choice of enclosing boundary conditions, the potentials and fields of two corners at equal and opposite potentials and displaced from each other by a distance equal to the gap length were superposed to map the potential and field for asymmetrical and symmetrical heads. For asymmetrical heads, the superposition approximation provided good agreement to finite-element calculations for the limited range of exterior corner angles 0 from 0 (right-angled corner) to 45, due to the mismatch of surface charge densities on both poles for this geometry. For symmetrical head structures, the superposition approximation was found to yield remarkable agreement to exact solutions for all gap corner orientations from 0 (right-angled head) to 90 ("thin" gap head). In the second method derived in this research for modelling asymmetrical heads involved using a rational function approximation with free parameters to model the surface potential of asymmetrical heads. The free parameters and their functional dependence on corner angle were determined through fitting to finite-element calculations, enabling the derivation of analytical expressions for the magnetic fields that are in good agreement with exact solutions for all corner angels (0 to 90). To complement the two approximate methods for modelling the fields from asymmetrical and symmetrical heads, a new general approach based on the sine integral transform was derived to model the reaction of soft underlayers on the surface potential or field of any two-dimensional head structure, for sufficiently close head-to-underlayer separations. This method produces an infinite series of correction terms whose coefficients are functions of the head-to-underlayer separation and gap corner angle, that are added to the surface potential or field in the absence of an underlayer. This new approach demonstrated good agreement with finite-element calculations for sufficiently close head-to-underlayer separations, and with the classical Green's functions solutions for increasing separations. Using the derived analytical method and explicit expressions in this work, an understanding of the nature of the magnetic fields and their spectra as functions of the gap corner angles is gained. This understanding and analytical theory will benefit the modelling, design and optimisation of high performance magnetic recording heads.

This diploma thesis deals with computing of edit influences on assigned stiff body from the flow of inviscid liquid. There are derived equations for computation of the influences during translational or torsional wobble and follow-up calculation of the units of their tensors.

La méthode que nous présentons pour modéliser des données dites de "comptage" ou données de Poisson est basée sur la procédure nommée Modélisation multi-niveau et interactive de la régression de Poisson (PRIMM) développée par Christiansen et Morris (1997). Dans la méthode PRIMM, la régression de Poisson ne comprend que des effets fixes tandis que notre modèle intègre en plus des effets aléatoires. De même que Christiansen et Morris (1997), le modèle étudié consiste à faire de l'inférence basée sur des approximations analytiques des distributions a posteriori des paramètres, évitant ainsi d'utiliser des méthodes computationnelles comme les méthodes de Monte Carlo par chaînes de Markov (MCMC). Les approximations sont basées sur la méthode de Laplace et la théorie asymptotique liée à l'approximation normale pour les lois a posteriori. L'estimation des paramètres de la régression de Poisson est faite par la maximisation de leur densité a posteriori via l'algorithme de Newton-Raphson. Cette étude détermine également les deux premiers moments a posteriori des paramètres de la loi de Poisson dont la distribution a posteriori de chacun d'eux est approximativement une loi gamma. Des applications sur deux exemples de données ont permis de vérifier que ce modèle peut être considéré dans une certaine mesure comme une généralisation de la méthode PRIMM. En effet, le modèle s'applique aussi bien aux données de Poisson non stratifiées qu'aux données stratifiées; et dans ce dernier cas, il comporte non seulement des effets fixes mais aussi des effets aléatoires liés aux strates. Enfin, le modèle est appliqué aux données relatives à plusieurs types d'effets indésirables observés chez les participants d'un essai clinique impliquant un vaccin quadrivalent contre la rougeole, les oreillons, la rub\'eole et la varicelle. La régression de Poisson comprend l'effet fixe correspondant à la variable traitement/contrôle, ainsi que des effets aléatoires liés aux systèmes biologiques du corps humain auxquels sont attribués les effets indésirables considérés. / We propose a method for analysing count or Poisson data based on the procedure called Poisson Regression Interactive Multilevel Modeling (PRIMM) introduced by Christiansen and Morris (1997). The Poisson regression in the PRIMM method has fixed effects only, whereas our model incorporates random effects. As well as Christiansen and Morris (1997), the model studied aims at doing inference based on adequate analytical approximations of posterior distributions of the parameters. This avoids the use of computationally expensive methods such as Markov chain Monte Carlo (MCMC) methods. The approximations are based on the Laplace's method and asymptotic theory. Estimates of Poisson mixed effects regression parameters are obtained through the maximization of their joint posterior density via the Newton-Raphson algorithm. This study also provides the first two posterior moments of the Poisson parameters involved. The posterior distributon of these parameters is approximated by a gamma distribution. Applications to two datasets show that our model can be somehow considered as a generalization of the PRIMM method since it also allows clustered count data. Finally, the model is applied to data involving many types of adverse events recorded by the participants of a drug clinical trial which involved a quadrivalent vaccine containing measles, mumps, rubella and varicella. The Poisson regression incorporates the fixed effect corresponding to the covariate treatment/control as well as a random effect associated with the biological system of the body affected by the adverse events.

Dans leur célèbre article de 1987, les physiciens Per Bak, Chao Tang et Kurt Wiesenfeld ont montré que certains systèmes complexes, composés d'un nombre important d'éléments en interaction dynamique, évoluent vers un état critique, sans intervention extérieure. Ce phénomène, appelé criticalité auto-organisée, peut être observé empiriquement ou simulé par ordinateur pour de nombreux modèles. Cependant leur analyse mathématique est très ardue. Même des modèles dont la définition est apparemment simple, comme les modèles décrivant la dynamique d'un tas de sable, ne sont pas bien compris mathématiquement. Le but de cette thèse est la construction d'un modèle de criticalité auto-organisée, qui est aussi simple que possible, et qui est accessible à une étude mathématique rigoureuse. Pour cela, nous modifions le modèle d'Ising Curie-Weiss généralisé en introduisant un contrôle automatique du paramètre de température. Pour une classe de distributions symétriques satisfaisant une certaine condition d'intégrabilité, nous montrons que la somme Sn des variables aléatoires du modèle a le comportement typique du modèle d'Ising Curie-Weiss généralisé critique: les fluctuations sont d'ordre n^(3/4) et la loi limite est C exp(- lambda*x^4) dx, où C et lambda sont des constantes strictement positives. Notre étude nous a menés à généraliser ce modèle dans plusieurs directions : cas de la dimension supérieure, fonctions d'interactions plus générales, extension à des auto-interactions menant à des fluctuations d'ordre n^(5/6). Nous étudions aussi des modèles dynamiques dont la distribution invariante est la loi de notre modèle d'Ising Curie-Weiss de criticalité auto-organisée. / In their famous 1987 article, Per Bak, Chao Tang and Kurt Wiesenfeld showed that certain complex systems, composed of a large number of dynamically interacting elements, are naturally attracted by critical points, without any external intervention. This phenomenon, called self-organized criticality, can be observed empirically or simulated on a computer in various models. However the mathematical analysis of these models turns out to be extremely difficult. Even models whose definition seems simple, such as the models describing the dynamics of a sandpile, are not well understood mathematically. The goal of this thesis is to design a model exhibiting self-organized criticality, which is as simple as possible, and which is amenable to a rigorous mathematical analysis. To this end, we modify the generalized Ising Curie-Weiss model by implementing an automatic control of the inverse temperature. For a class of symmetric distributions whose density satisfies some integrability conditions, we prove that the sum Sn of the random variables behaves as in the typical critical generalized Ising Curie-Weiss model: the fluctuations are of order n^(3/4) and the limiting law is C exp(- lambda*x^4) dx where C and lambda are suitable positive constants. Our study led us to generalize this model in several directions: the multidimensional case, more general interacting functions, extension to self-interactions leading to fluctuations with order n^(5/6). We also study dynamic models whose invariant distribution is the law of our Curie-Weiss model of self-organized criticality.

La méthode que nous présentons pour modéliser des données dites de "comptage" ou données de Poisson est basée sur la procédure nommée Modélisation multi-niveau et interactive de la régression de Poisson (PRIMM) développée par Christiansen et Morris (1997). Dans la méthode PRIMM, la régression de Poisson ne comprend que des effets fixes tandis que notre modèle intègre en plus des effets aléatoires. De même que Christiansen et Morris (1997), le modèle étudié consiste à faire de l'inférence basée sur des approximations analytiques des distributions a posteriori des paramètres, évitant ainsi d'utiliser des méthodes computationnelles comme les méthodes de Monte Carlo par chaînes de Markov (MCMC). Les approximations sont basées sur la méthode de Laplace et la théorie asymptotique liée à l'approximation normale pour les lois a posteriori. L'estimation des paramètres de la régression de Poisson est faite par la maximisation de leur densité a posteriori via l'algorithme de Newton-Raphson. Cette étude détermine également les deux premiers moments a posteriori des paramètres de la loi de Poisson dont la distribution a posteriori de chacun d'eux est approximativement une loi gamma. Des applications sur deux exemples de données ont permis de vérifier que ce modèle peut être considéré dans une certaine mesure comme une généralisation de la méthode PRIMM. En effet, le modèle s'applique aussi bien aux données de Poisson non stratifiées qu'aux données stratifiées; et dans ce dernier cas, il comporte non seulement des effets fixes mais aussi des effets aléatoires liés aux strates. Enfin, le modèle est appliqué aux données relatives à plusieurs types d'effets indésirables observés chez les participants d'un essai clinique impliquant un vaccin quadrivalent contre la rougeole, les oreillons, la rub\'eole et la varicelle. La régression de Poisson comprend l'effet fixe correspondant à la variable traitement/contrôle, ainsi que des effets aléatoires liés aux systèmes biologiques du corps humain auxquels sont attribués les effets indésirables considérés. / We propose a method for analysing count or Poisson data based on the procedure called Poisson Regression Interactive Multilevel Modeling (PRIMM) introduced by Christiansen and Morris (1997). The Poisson regression in the PRIMM method has fixed effects only, whereas our model incorporates random effects. As well as Christiansen and Morris (1997), the model studied aims at doing inference based on adequate analytical approximations of posterior distributions of the parameters. This avoids the use of computationally expensive methods such as Markov chain Monte Carlo (MCMC) methods. The approximations are based on the Laplace's method and asymptotic theory. Estimates of Poisson mixed effects regression parameters are obtained through the maximization of their joint posterior density via the Newton-Raphson algorithm. This study also provides the first two posterior moments of the Poisson parameters involved. The posterior distributon of these parameters is approximated by a gamma distribution. Applications to two datasets show that our model can be somehow considered as a generalization of the PRIMM method since it also allows clustered count data. Finally, the model is applied to data involving many types of adverse events recorded by the participants of a drug clinical trial which involved a quadrivalent vaccine containing measles, mumps, rubella and varicella. The Poisson regression incorporates the fixed effect corresponding to the covariate treatment/control as well as a random effect associated with the biological system of the body affected by the adverse events.

Orientador: Andre Koch Torres de Assis / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Fisica Gleb Wataghin / Made available in DSpace on 2018-08-04T04:12:38Z (GMT). No. of bitstreams: 1 Hernandes_JulioAkashi_D.pdf: 11255919 bytes, checksum: 8c053f16e5fd883058c7336bb38c3acc (MD5) Previous issue date: 2005 / Resumo: No Capítulo 1 apresentamos uma introdução sobre os campos elétricos dentro e fora de condutores resistivos com corrente constante. Discutimos também a distribuição de cargas superficiais que mantém a corrente fluindo e sua relação com estes campos elétricos. São apresentados alguns experimentos relacionados com estes campos elétricos fora de condutores com corrente constante. A Parte I deste trabalho trata de condutores retos e compridos. No Capítulo 2 apresentamos o tratamento de um fio cilíndrico longo de seção reta circular conduzindo uma corrente estacionária, já conhecido na literatura. São apresentados alguns dos métodos que seguimos nos tratamentos dos problemas apresentados a seguir. O Capítulo 3 trata da força entre uma casca cilíndrica condutora infinita sem corrente e uma carga pontual próxima (dentro ou fora da casca), cuja solução é inédita na literatura. Esta força de ordem zero (eletrostática) complementa a análise da força de primeira ordem ( ou seja, proporcional à corrente ou à velocidade dos elétrons de condução) no caso do fio cilíndrico longo com corrente constante. No Capítulo 4 tratamos o problema inédito de um fio cilíndrico longo, ainda conduzindo uma corrente estacionária, mas agora com uma bateria colocada no centro. Nosso objetivo aqui é estudar o comportamento dos campos e das cargas superficiais próximas à bateria. O Capítulo 5 apresenta o problema conhecido na literatura de placas retas conduzindo correntes estacionárias. Este problema foi tratado por este mesmo autor durante sua dissertação de mestrado. O comportamento dos campos e das cargas superficiais próximas a uma bateria no problema de condutores em forma de placas é abordado no Capítulo 6. Este também é um problema inédito na literatura, análogo ao problema tratado no Capítulo 4. No Capítulo 7 generalizamos o problema das placas com corrente constante utilizando agora uma fita de largura finita. Para resolver este problema inédito utilizamos coordenadas elíptico-cilíndricas. Com este caso encerramos nosso tratamento de problemas onde os condutores são retos e compridos, conduzindo correntes na direção longitudinal. Na Parte II tratamos de condutores curvos conduzindo correntes constantes na direção azimutal. Estes problemas são importantes porque representam uma classe de circuitos elétricos em que a corrente percorre um caminho fechado finito. O Capítulo 8 apresenta o problema conhecido na literatura de uma casca cilíndrica condutora de comprimento infinito conduzindo uma corrente estacionária na direção azimutal. Há uma bateria em forma de linha, paralela ao eixo da casca. Esta geometria tem solução bastante simples com forma analítica fechada para o potencial, para o campo elétrico e para as cargas superficiais, embora o cilindro tenha comprimento infinito. O Capítulo 9 apresenta o tratamento inédito para uma casca esférica resistiva conduzindo uma corrente estacionária. Neste caso, a bateria tem a forma de um segmento de linha (um meridiano da esfera). O problema mais complexo de um toróide condutor conduzindo uma corrente constante na direção azimutal, também novo na literatura, é apresentado no Capítulo 10. Estes dois problemas, da casca esférica e do toróide, representam duas situações onde não há infinitos na geometria nem na condutividade, sendo que a corrente está confinada em um espaço finito. Mesmo abateria está incluída no sistema, de modo que se obtém naturalmente o comportamento esperado dos campos e das cargas superficiais próximas a ela. Na Parte III fazemos uma discussão sobre os problemas tratados. Demonstramos que para todos os casos analisados existe um campo elétrico fora dos condutores com corrente constante e obtemos sua expressão analítica. Os comportamentos em todos os casos em que a bateria está presente foram encontrados de acordo com o esperado. As comparações que fizemos com experimentos da literatura mostraram que nossos resultados teóricos são razoáveis e coerentes / Abstract: In Chapter 1 we present an introduction about the electric field inside and outside resistive conductors carrying steady currents. We also discuss the distribution of surface charges that maintains the current fiow and its relation with these electric fields. We present some experiments related with these electric fields outside conductors with steady current. Part I of this work deals with long straight conductors. In Chapter 2 we present the treatment of a long cylindrical wire of circular cross section conducting a steady current, already known in the literature. We present some of the methods that we employ in the problems that follow. Chapter 3 deals with the force between an infinite cylindrical conducting shell without current and a point charge close by (inside or outside the shell). This solution is new in the literature. This force of zeroth order (electrostatics) complements the analysis of the first order force (i.e., proportional to the current or to the drifting velocity of the conduction electrons) in the case of the long cylindrical wire with steady current. Chapter 4 deals with the new problem of a long straight wire, still with a steady current, but now with a battery in the middle. Our objective here is to study the behaviour of the fields and of the surface charges near the battery. Chapter 5 presents the known problem of straight plates conducting steady currents. This problem was dealt with by the present author during his Master's Degree. The behaviour of the fields and of the surface charges near the battery in the problem of conductors in the shape of plates is approached in Chapter 6. This is also a new problem in the literature, analogous to the problem treated in Chapter 4. In Chapter 7 we generalize the problem of plates with steady currents utilizing now a strip of finite width. To solve this new problem we utilize elliptic-cylindrical coordinates. With this case we finish our treatment of problems of long and straight conductors, carrying currents in the longitudinal direction. In Part II we treat curved conductors with steady currents in the azimuthal direction. These problems are important because they represent a class of electric circuits in which the current fiows over a closed finite path. Chapter 8 presents the known problem of a conducting cylindrical shell of infinite length carrying a steady current in the azimuthal direction. There is a battery in the shape of aline, parallel to the axis of the shell. This geometry yields a very simple solution with a closed analytical form for the potential, electric field and surface charges, although the cylinder has an infinite length. Chapter 9 presents the new treatment of a resistive spherical shell with a steady current. In this case, the battery has the shape of a segment of line ( a meridian of the sphere). The more complex problem of a conducting toroid with a steady current in the azimuthal direction, also new in the literature, is presented in Chapter 10. These two problems, about the spherical shell and the toroid, represent two situations where there are no infinities in the geometry nor in the conductivity, while the current is confined in a finite space Even the battery is included in the system, so that we obtain naturally the expected behaviour of the fields and of the surface charges near the battery. In Part III we present a discussion of the problems treated here. We demonstrate that for all the analysed cases there is an electric field outside the conductors with steady currents and we obtain their expressions analytically. The behaviours of all cases in which the battery was present were found according to our expectations. The comparisons that we made with experiments of the literature showed that our theoretical results are reasonable and coherent / Doutorado / Física / Doutor em Ciências

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